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diff --git a/Master/texmf-dist/doc/latex/lapdf/trochoid.tex b/Master/texmf-dist/doc/latex/lapdf/trochoid.tex new file mode 100644 index 00000000000..b76b527b4fe --- /dev/null +++ b/Master/texmf-dist/doc/latex/lapdf/trochoid.tex @@ -0,0 +1,78 @@ +\input preamble.tex + +\Defnum(\n,0) +\Defdim(\m,-2.5) +\newdimen\x +\newdimen\y + +% --------------------------------------------------------------------------- +% 1. Trochoids: In case of a=b the graph is a cycloid. +% x(t)=a*t-b*sint +% y(t)=a-b*cost +% --------------------------------------------------------------------------- +\def\Trochoid(#1,#2){ +\def\Tx(##1,##2){\Dset(##2,##1) ##2=#1##2 \Sin(##1,\y) \y=#2\y \Sub(##2,\y)} +\def\Ty(##1,##2){\Dset(##2,#1) \Cos(##1,\y) \y=#2\y \Sub(##2,\y)} +\Tplot(200)(-6.2832,6.2832)} + +% --------------------------------------------------------------------------- +% 2. Epitrochoid: +% x(t)=a*cos(t)-b*cos(a/2*t) +% y(t)=a*sin(t)-b*sin(a/2*t) +% --------------------------------------------------------------------------- +\def\Epitrochoid(#1,#2){\Dset(\x,#1) \x=0.5\x + \def\Tx(##1,##2){\Cos(##1,##2) ##2=#1##2 \y=##1\x \Cos(\Np\y,\y) \y=#2\y \Sub(##2,\y) ##2=0.5##2} + \def\Ty(##1,##2){\Sin(##1,##2) ##2=#1##2 \y=##1\x \Sin(\Np\y,\y) \y=#2\y \Sub(##2,\y) ##2=0.5##2} + \Tplot(360)(0,12.5664)} + +% --------------------------------------------------------------------------- +% 3. Hypotrochoid: +% x(t)=a*cos(t)+b*cos(a/2*t) +% y(t)=a*sin(t)-b*sin(a/2*t) +% --------------------------------------------------------------------------- +\def\Hypotrochoid(#1,#2){\Dset(\x,#1) \x=0.5\x + \def\Tx(##1,##2){\Cos(##1,##2) ##2=#1##2 \y=##1\x \Cos(\Np\y,\y) \y=#2\y \Add(##2,\y) ##2=0.5##2} + \def\Ty(##1,##2){\Sin(##1,##2) ##2=#1##2 \y=##1\x \Sin(\Np\y,\y) \y=#2\y \Sub(##2,\y) ##2=0.5##2} + \Tplot(360)(0,12.5664)} + +% --------------------------------------------------------------------------- +\begin{document} +\unitlength1.25cm + +\begin{center} +{\Huge \bf{I. Trochoids}} +\bigskip + +\begin{lapdf}(14,7)(-7,-2) + \Lingrid(10)(0,2)(-7,7)(-2,4) + \Whiledim{\m<3}{\Stepcol(0,23,4) \Trochoid(1,\Np\m) \Stroke \Dadd(\m,0.5)} +\end{lapdf} + +$x(t)=a \cdot t - b\sin(t)$ \qquad$y(t)=a-b\cos(t)$ + +\newpage + +{\Huge\bf{II. Epitrochoids}} +\bigskip + +\begin{lapdf}(14,14)(-7,-7) + \Polgrid(0,2)(7) + \Whilenum{\n<6}{\Stepcol(0,23,4) \Epitrochoid(8,\n) \Stroke \Add(\n,1)} +\end{lapdf} + +$x(t)=a\cos(t)-b\cos(a/2 \cdot t)$ \qquad $y(t)=a\sin(t)-b\sin(a/2 \cdot t)$ + +\newpage + +{\Huge\bf{III. Hypotrochoids}} +\bigskip + +\begin{lapdf}(14,14)(-7,-7) + \Resetcol + \Polgrid(0,2)(7) + \Whilenum{\n<6}{\Stepcol(0,23,4) \Hypotrochoid(8,\n) \Stroke \Add(\n,1)} +\end{lapdf} + +$x(t)=a\cos(t)+b\cos(a/2 \cdot t)$ \qquad $y(t)=a\sin(t)-b\sin(a/2 \cdot t)$ +\end{center} +\end{document} |